Compressed sensing is a collection of techniques for recovering sparse signal and image data from under-sampled data. Traditionally, one requirement for the compressed sensing techniques is that data must be incoherence. Random sampling schemes obey such requirements. However, when working with MRI systems, random sampling is impractical and can potentially hurt the acquisition time due to the physical limitations of present in MRI systems generally and human philological limitations.
Recent theoretical work has shown compressed sensing is possible when data is asymptotically incoherent. As is understood in the art, signal coherence decreases as either the Fourier frequency or wavelet scale increases. Thus, in the MRI domain, incoherence can be asymptotically achieved by increasing the number of high-frequency samples in k-space. Asymptotic incoherence allows one to achieve the benefits of compressed sensing, including significantly sub-sampling the data space, where complete incoherence cannot be achieved. However, to date, asymptotically incoherence has only been demonstrated in simulated environments where the location of sampling points is not limited due to real-world hardware and physiological constraints. Thus, it is desired to create a framework for the selection of optimal sampling strategies applicable to exploiting the asymptotic incoherence properties of image data in real-world scenarios.